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# If |x–1|<4, so:

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Intern
Joined: 26 Feb 2017
Posts: 29
Location: Brazil
GMAT 1: 610 Q45 V28
GPA: 3.11

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24 Oct 2017, 04:10
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Difficulty:

85% (hard)

Question Stats:

32% (01:09) correct 68% (01:17) wrong based on 572 sessions

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If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above
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Joined: 02 Sep 2009
Posts: 58449

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24 Oct 2017, 04:13
2
7
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

$$|x–1|<4$$;

$$-4<x-1<4$$;

$$-3<x<5$$.

Any x from that range will be more than -4.

P.S. What is the source of this question?
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##### General Discussion
Intern
Joined: 26 Feb 2017
Posts: 29
Location: Brazil
GMAT 1: 610 Q45 V28
GPA: 3.11

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24 Oct 2017, 04:24
1
Bunuel wrote:
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

$$|x–1|<4$$;

$$-4<x-1<4$$;

$$-3<x<5$$.

Any x from that range will be more than -4.

P.S. What is the source of this question?

Bunnel,

First of all, thank you very much.

The source of this questions is a bank of questions that I received from a friend, whose his teacher gave to him.

I have huge doubts on inequalities topics.

As you explained above any value X>-4 can satisfy this.

What is the best approach to deal with this kind of questions? I solved -3<x<5, but I could not figure out, X>-4 because -3>-4 and do not satisfy the inequality.

I have the same doubt on this question, below...

https://gmatclub.com/forum/if-z-2-4z-5- ... l#p1949237
Math Expert
Joined: 02 Sep 2009
Posts: 58449

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24 Oct 2017, 04:27
1
2
vitorpteixeira wrote:
Bunuel wrote:
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

$$|x–1|<4$$;

$$-4<x-1<4$$;

$$-3<x<5$$.

Any x from that range will be more than -4.

P.S. What is the source of this question?

Bunnel,

First of all, thank you very much.

The source of this questions is a bank of questions that I received from a friend, whose his teacher gave to him.

I have huge doubts on inequalities topics.

As you explained above any value X>-4 can satisfy this.

What is the best approach to deal with this kind of questions? I solved -3<x<5, but I could not figure out, X>-4 because -3>-4 and do not satisfy the inequality.

I have the same doubt on this question, below...

https://gmatclub.com/forum/if-z-2-4z-5- ... l#p1949237

It's the other way around. We know that $$-3<x<5$$. Any x from that range satisfy x > -4.

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25 Oct 2017, 10:40
Bunuel wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

$$|x–1|<4$$;

$$-4<x-1<4$$;

$$-3<x<5$$.

Any x from that range will be more than -4.

P.S. What is the source of this question?[/quote]

Hi, Bunuel
Just wanted to ask that since in this question it is not mentioned that x is an integer, by the range x>-4 it will include values greater than -3 also (say -3.8) but our range is from -3 to 5 so isnt this wrong????
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Joined: 02 Sep 2009
Posts: 58449

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25 Oct 2017, 10:51
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26 Oct 2017, 15:47
1
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

We can solve the inequality when (x - 1) is positive and when it is negative.

When (x - 1) is positive:

x - 1 < 4

x < 5

When (x - 1) is negative:

-x + 1 < 4

-x < 3

x > -3

-3 < x < 5

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Manager
Joined: 15 Feb 2017
Posts: 76

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26 Oct 2017, 17:53
4
IMO Option D is the right answer.
|x-1|<4 means
-4<x-1<4
-3<x<5
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Joined: 05 Dec 2016
Posts: 236
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29

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27 Oct 2017, 05:01
It's a tricky question, I think I've encountered a sort of this one in OG2017.
Key to solve it is to find the range from the answer choices that covers all possible values of x,here it is answer choice D.
Intern
Joined: 24 Nov 2016
Posts: 30

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27 Oct 2017, 11:03
1
I can't understand why x>-4 is the correct answer.

Since we have -3<x<5 , -3 is out of the range and in x> -4 -3 is included in the number line.

Besides that, X>-4 we can have x=10, as an exemple, wich is not true since x<5.

Can someone help me with this points?

tks
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Joined: 07 Jul 2017
Posts: 9

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01 Nov 2017, 08:13
Bunuel wrote:
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

$$|x–1|<4$$;

$$-4<x-1<4$$;

$$-3<x<5$$.

Any x from that range will be more than -4.

P.S. What is the source of this question?

Hi Bunuel, thanks for the explanation. I tend to approach this questions in the wrong way, trying to find an answer choice that matches with the range found through the inequalities. For instance, in this case I was looking for -3<x<5 (or something more restrictive, such as -2 < x < -5), which led me to pick answer E.

Given your explanation, I understand that I should look for that condition that holds for every x in the range...but I still have a huge doubt.
You say it is (D) x > -4 because any X from that range will be more than -4. Following your logic, wouldn't also B) x ≤ 4 be true? Our range is -3<x<5, which means that every x will be less or equal to 4.

Is there something I am not getting right?

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Joined: 02 Sep 2009
Posts: 58449

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01 Nov 2017, 09:53
1
delid wrote:
Bunuel wrote:
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

$$|x–1|<4$$;

$$-4<x-1<4$$;

$$-3<x<5$$.

Any x from that range will be more than -4.

P.S. What is the source of this question?

Hi Bunuel, thanks for the explanation. I tend to approach this questions in the wrong way, trying to find an answer choice that matches with the range found through the inequalities. For instance, in this case I was looking for -3<x<5 (or something more restrictive, such as -2 < x < -5), which led me to pick answer E.

Given your explanation, I understand that I should look for that condition that holds for every x in the range...but I still have a huge doubt.
You say it is (D) x > -4 because any X from that range will be more than -4. Following your logic, wouldn't also B) x ≤ 4 be true? Our range is -3<x<5, which means that every x will be less or equal to 4.

Is there something I am not getting right?

For $$-3<x<5$$, (B) x ≤ 4 won't always be true. For example, x could be 4.5 (4.5 IS between -3 and 5) and in this case B is not true.
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04 Nov 2017, 04:02
|x–1|<4

−3<x<5

Any x from that range will be more than -4.

Math Expert
Joined: 02 Sep 2009
Posts: 58449

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14 Jan 2018, 23:12
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

Check other similar questions from Trickiest Inequality Questions Type: Confusing Ranges (part of our Special Questions Directory).
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26 Mar 2018, 15:50
Wouldn't this question be better off as a "which of the following must be true" question? Does the actual test do stuff like this?
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Joined: 10 Jun 2019
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20 Jun 2019, 05:49
On solving the inequality, we get x<5 and x>-3.
Among the options, we have x>-4, which is already satisfied given that x>-3 and since -4<-3, we can conclude that x>-4.
Hence, Option D is the right choice.
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Joined: 12 Apr 2019
Posts: 268

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21 Jun 2019, 05:31
delid wrote:
Bunuel wrote:
vitorpteixeira wrote:
If |x–1|<4, so:

(A) x > 3
(B) x ≤ 4
(C) -4< x < 4
(D) x > -4
(E) none of the above

$$|x–1|<4$$;

$$-4<x-1<4$$;

$$-3<x<5$$.

Any x from that range will be more than -4.

P.S. What is the source of this question?

Hi Bunuel, thanks for the explanation. I tend to approach this questions in the wrong way, trying to find an answer choice that matches with the range found through the inequalities. For instance, in this case I was looking for -3<x<5 (or something more restrictive, such as -2 < x < -5), which led me to pick answer E.

Given your explanation, I understand that I should look for that condition that holds for every x in the range...but I still have a huge doubt.
You say it is (D) x > -4 because any X from that range will be more than -4. Following your logic, wouldn't also B) x ≤ 4 be true? Our range is -3<x<5, which means that every x will be less or equal to 4.

Is there something I am not getting right?

Although this is a relatively simple question on absolute values (modulus), the way in which the options have been framed can put you off.

The reason for this is that, you go in to the solution, expecting to see a range that you think you’ll get when you solve the given inequality. But, in reality, none of the options represent the exact range that you will get when you solve the inequality.
Therefore, it becomes important to understand that , here, we are trying to find out a range of values, which in turn fully covers the range which satisfies the given inequality.

If |x-a| < y, the range of x that satisfies the inequality will be a-y < x < a+y. When we apply this to the given inequality, |x-1| < 4, we can say that -3<x<5. Let us represent this on a number line, as shown below:

Attachment:

21st June 2019 - Reply 3 - 1.JPG [ 14.93 KiB | Viewed 989 times ]

Let us evaluate the options now.

Option 1 says x>3. This means that x can be any value from 3 to infinity. Clearly, only a portion of this range satisfies our inequality i.e. 3<x<5.
So, quite obviously, you cannot say that all values which satisfy |x-1|<4 fall in the range of x>3.

Attachment:

21st June 2019 - Reply 3 - 2.JPG [ 16.29 KiB | Viewed 990 times ]

A similar thing works against option B.

With option C, although some numbers are within the range, some numbers aren’t. Like for example, x = 4.5 satisfies the given inequality but is not within -4<x<4.

When it comes to option D, we can say that all the values that satisfy our inequality are greater than -4. This means, when I pick any value from the range satisfying the inequality, it will always qualify as true when compared with option D.

The same cannot be said about the other options, as we have demonstrated.
So, the correct answer is D.

The confusion that this question has created could have been nullified if the question was framed as a ‘Must be’ question. For example “ If |x-1|<4, which of the following must be true for the values of x that satisfy the inequality?” . Essentially, this is what the question is testing you on.

Hope this helps!
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Re: If |x–1|<4, so:   [#permalink] 21 Jun 2019, 05:31
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